Let x # hotel bill (before taxes) for City # 1
Let y = hotel bill (before taxes) for City # 2
Equation # 1: Hotel charge for 2nd city was $1,500 higher than for the first city, can be stated as:
- x + y = 1,500
Equation # 2: The 4% tax on City # 1 hotel bill + 3.5% on City # 2 hotel bill, totaled $371.25, can be stated as:
0.04x + 0.035y = 371.25
One can either do substitution, or set these up in a matrix format. If one were to simply do the substitution format, then:
-x + y = 1,500
+x +x
y = x + 1,500
Go to the 2nd equation, and where see "y", substitute in: x + 1,500
0.04x + 0.035 (x + 1,500) = 371.25
0.04x + 0.035x + 52.5 = 371.25
Next, collect like terms on the left; substract out 52.5 from both sides, to get:
0.075x = 318.75
To solve for x (money for hotel in City # 1, before taxes), divide out both sides by: 0.075, to get:
x = $4,250
To find 'y', substitute the x-value (4,250) back into the first equation:
-4,250 + y = 1,500
Add 4,250 to both sides, to get:
y = 5,750
So, amount spent in City # 1 before taxes was: 4,250
amount spent in City # 2 before taxes was: 5,750
Checks:
Check # 1: -4,250 + 5,750 = 1,500 [Check]
Check # 2: 0.04*4,250 + 0.035*5,750 + 371.25
170 + 201.25 = 371.25
371.25 = 371.25 [Check]
